Yes it would be a great experience.It would be hot though.You would certainly find peace there in the mountains/hills/monastries.Please think carefully before opting to climb Tigers Nest hill with small children.It is a tough hike for sure.
Bhutan is great country to visit. To have local feel you must visit Haa valley and Punakha valley. I'll suggest to book Homestays in those places. People are very helpful and calm. And one thing I'll suggest is to let your kids observe the social behavior of those people, it's amazing!!! For any further details feel free to contact!!! Best luck for your adventure!